Posted by Kayleigh on .
Consider the functions
f(x)= 5x+4/x+3(This is a fraction) and
g(x)= 3x4/5x(This is a fraction)
a)Find f(g(x))
b)Find g(f(x))
c)Determine whether the functions f and g are inverses of each other.

Consider the functions 
Steve,
f(g) = (5g+4)/(g+3)
= (5(3x4)/(5x)+4) / ((3x4)/(5x)+3)
= x
g(f) = (3f4)/(5f)
= (3((5x+4)/(x+3))4) / (5((5x+4)/(x+3)))
= x
since f(g) = g(f) = x, they are inverses 
Consider the functions 
Kayleigh,
What are the values that need to be excluded?

Consider the functions 
Steve,
whatever makes the denominator zero must be excluded, since division by zero is undefined.
So, for f(g), x=5 is not allowed, since g(5) is not defined. In addition, since f(3) is not defined, any x where g(x) = 3 must also be excluded. Luckily, there is no such x.
Use similar reasoning for g(f). 
Consider the functions 
Kayleigh,
So there are no values to be excluded?

Consider the functions 
Steve,
Read what I said. You have to exclude x=5 because g(5) is not defined. Therefore, f(g(5)) is also not defined.